Rich Audu hit a pair of key 3-pointers in the second half for the Saints (4-13, 2-4), who had lost 11 in a row before defeating Canisius 57-54 Friday night.
Saint Peter's (6-10, 1-5) fell behind by 13 points in the first half but trailed just 49-47 with 5:07 remaining.
Siena ran off the next eight points, including consecutive treys by Audu, who played the rest of the way after Ryan Oliver injured his knee in the game's second minute.
The Saints had a huge edge in free throws, making 27 of 36, while Saint Peter's made 5 of 12. Anosike, who was averaging 45.8 percent from the line, made 12 of 17.
Desi Washington led the Peacocks with 16 points.
Mike Krzyzewski says he has good reason to be excited for next season thanks to a combination of Duke's incoming freshmen and a core of experienced upperclassmen.
Georgia guard Juwan Parker has been awarded a medical redshirt, leaving him with two years of eligibility, after missing the 2015-16 season with a partially torn Achilles tendon.
Forward Trevon Bluiett has withdrawn from consideration from the NBA draft and will return to Xavier for his junior season.